Long-Run Costs

We have described the firm’s short-run cost function in tabular and graphic forms. The cost function also can be represented in equation form. The repair company’s short-run cost function is

C C(Q) 270 (30Q .3Q2), [6.2]

where output is measured in thousands of units and costs are in thousands of dollars. (You should check this equation against Figure 6.1 for various outputs.) The first term is the firm’s fixed costs; the term in parentheses encompasses its variable costs. In turn, short-run average cost is SAC C/Q, or

SAC 270/Q (30 .3Q). [6.3]

The first term usually is referred to as average fixed cost (fixed cost divided by total output); the term in the parentheses is average variable cost (variable cost divided by total output). According to Equation 6.3, as output increases, average fixed cost steadily declines while average variable cost rises. The first effect dominates for low levels of output; the second prevails at sufficiently high levels. The combination of these two effects explains the U-shaped average cost curve. Finally, treating cost as a continuous function, we find marginal cost to be

SMC dC/dQ 30 .6Q. [6.4]

We observe that marginal cost rises with the level of output.

In the long run, the firm can freely vary all of its inputs. In other words, there are no fixed inputs or fixed costs; all costs are variable. Thus, there is no difference between total costs and variable costs. We begin our discussion by stressing two basic points. First, the ability to vary all inputs allows the firm to produce at lower cost in the long run than in the short run (when some inputs are fixed). In short, flexibility is valuable. As we saw in Chapter 5, the firm still faces the task of finding the least-cost combination of inputs.

Second, the shape of the long-run cost curve depends on returns to scale. To see this, suppose the firm’s production function exhibits constant returns to scale. Constant returns to scale means that increasing all inputs by a given percentage (say, 20 percent) increases output by the same percentage. Assuming input prices are unchanged, the firm’s total expenditure on inputs also will increase by 20 percent. Thus, the output increase is accompanied by an equal percentage increase in costs, with the result that average cost is unchanged. As long as constant returns prevail, average cost is constant.

Production exhibits increasing returns to scale or, equivalently, economies of scale if average cost falls as the firm’s scale of operation increases. For instance, a 20 percent increase in all inputs generates a greater than 20 percent increase in output, causing average cost per unit to fall. When increasing returns prevail, average cost falls as output increases. Finally, decreasing returns to scale prevail if increasing all inputs by a given percentage amount results in a less than proportional increase in output. It follows that the presence of decreasing returns to scale implies rising average costs as the firm’s output and scale increase.

SHORT-RUN VERSUS LONG-RUN COST Consider a firm that produces output using two inputs, labor and capital. Management’s immediate task is to plan for future production. It has not leased plant and equipment yet, nor has it hired labor. Thus, it is free to choose any amounts of these inputs it wishes. Management knows that production exhibits constant returns to scale. Consequently, the firm’s long-run average cost (LAC) is constant as shown by the horizontal line in Figure 6.3. Furthermore, we can show that the firm should plan to use the same optimal ratio of labor to capital in production, regardless of the level of

Long-Run Average Cost $5

4 SAC1 (9,000 ft2 plant)

SMC1 SMC2 SAC2 (18,000 ft2 plant)

SMC3 SAC3 (27,000 ft2 plant)

FIGURE 6.3

Short-Run versus Long-Run Cost

Under constant returns to scale, the firm’s LAC is constant. However, SACs depend on the size of the firm’s plant and are U-shaped.

LAC = LMC

0 72 108 144

216 Output (Thousands of Units)

Comparative Advantage and International Trade

output. If the firm plans to double its level of output, it should also double the use of each input, leaving the proportions unchanged. These input proportions (in combination with prevailing input prices) determine the firm’s average cost per unit. In Figure 6.3, LAC C/Q $4. The long-run total cost function is C 4Q. Thus, long-run marginal cost (LMC) is also $4 per unit. As the figure shows, long-run marginal and average costs are constant and identical.

Figure 6.3 also shows the short-run average cost curves for three possible plants of varying sizes. The firm’s plant (and equipment therein) represents the total capital input. The left curve is for a 9,000-square-foot plant, the middle curve for an 18,000-square-foot plant, and the right curve for a 27,000-squarefoot plant. Notice that the smallest plant is optimal for producing 72,000 units of output. With such a plant in place (and using the right amount of labor), the firm can produce this output level at a minimum average cost of $4. If the firm planned to produce twice the level of output (144,000 units), it would use a plant twice the size (an 18,000-square-foot facility) and twice the labor. Finally, the largest plant is optimal for producing 216,000 units.

Once its plant is in place, however, the firm has considerably less flexibility. In the short run, its plant cannot be varied. Thus, if a 9,000-square-foot plant is in place, production of an output, such as 108,000 units (see Figure 6.3), means an increase in the average cost of production above $4. Why? To produce this output requires expanding the use of labor (since the plant is fixed). Because of diminishing returns, the extra output comes at an increasing marginal cost, and this drives up average cost as well.

Obviously, the firm may have many choices of plant size, not just three. Before its plant is in place, the firm has complete flexibility to produce any level of output at a $4 unit cost. It simply builds a plant of the proper scale and applies the right proportion of labor. In this long-run planning horizon, it enjoys complete flexibility as to the scale of production. However, once the plant is built and in place, any change in planned output must be achieved by a change in labor (the sole variable input). The result is a movement either right or left up the U of the relevant SAC curve. In either case, there is an increase in average cost.

In a host of industries, such as electronics, automobiles, computers, aircraft, and agricultural products of all kinds, competition is worldwide. The major industrial countries of the world compete with one another for shares of global markets. For numerous goods, a U.S. consumer has a choice of purchasing a domestically produced item or a comparable imported good made in a farflung corner of the world—for instance, Europe, East Asia, or South America. Thus, a knowledge of international trade is essential for successful managers in increasingly global industries.

International trade is based on mutually beneficial specialization among countries. Why does one country concentrate on production and exports in

certain goods and services, and another country specialize in others? Important reasons for varying patterns of specialization include different resource endowments, differences in the amount and productivity of labor, and differences in capital. For instance, a nation with abundant agricultural resources, predominantly unskilled labor, and little capital is likely to specialize in production of basic foods. By contrast, a nation, such as Japan, with a highly educated population and abundant capital but with relatively few natural resources, has an advantage in manufactured goods. Many observers believe that the United States’ competitive advantage lies in high-tech goods and services. Relying on their research expertise and innovative ability, American firms excel in the development of technologically advanced goods and services. As these markets grow and mature, however, one would expect high-tech goods to evolve into commodity items, assembled and produced in large-scale facilities. It is not surprising that production of these goods tends to shift to other parts of the world over time.

To understand the basis for mutually beneficial trade, it is important to grasp the notion of comparative advantage. The easiest way to explain this concept is with a simple example. Table 6.2 offers a stylized depiction of trade involving two goods, digital electronic watches and pharmaceutical products, and two countries, the United States and Japan. Part (a) of the table shows the productivity of labor (that is, output per hour) in each country for each good. For instance, on average U.S. workers produce 4 bottles of pills and 1 digital watch per labor-hour; their Japanese counterparts produce 2 bottles and .8 watches per labor-hour. According to the table, the United States is a more efficient manufacturer of both items; that is, U.S. workers are more productive in both sectors.

However, labor productivity is only one factor influencing the cost of production. The other determinant is the price of the input, in this case, the price of labor. To compute the labor cost per unit of output, we need to know the prevailing hourly wage in each country. To keep things simple, suppose the U.S. wage in both sectors is $15 per hour, whereas the Japanese wage in both sectors is 1,000 yen (¥) per hour. Naturally, the Japanese wage is denominated in that country’s currency, the yen. Now consider the labor cost per unit of each good in each country. For the U.S. pharmaceutical sector, this labor cost is simply ($15 per hour)/(4 bottles per hour) $3.75 per bottle, using Equation 6.1. Part (b) of the table lists these costs for each country. For Japan, the cost in yen is shown in parentheses. For example, the labor cost per digital watch is 1,000/.8 ¥1,250.

Finally, to make cross-country cost comparisons, we need one additional piece of information: the prevailing exchange rate between the two currencies. As its name suggests, the exchange rate denotes the amount of one country’s currency that exchanges for a unit of another country’s. Again, keeping things simple, suppose the current exchange rate in round numbers is 100 yen per dollar. (Furthermore, we suppose that this rate is expected to remain unchanged.) Using this exchange rate, it is a simple matter to convert the countries’ costs per unit into a common currency, in this case the dollar. Japan’s

TABLE 6.2

Relative Costs in the United States and Japan

a. Productivity

Pharmaceuticals Digital Watches

United States 4 per hour 1 per hour Japan 2 .8

b. Costs

Pharmaceuticals Digital Watches

United States $3.75 per bottle $15 per watch Japan $5.00 $12.50 (¥500) (¥1,250)

labor cost per bottle is ¥500, or $5.00 after dividing by the exchange rate of ¥100 per dollar. Similarly, its cost per digital watch is ¥1,250, or $12.50. Table 6.2b lists these conversions.

Table 6.2 conveys a specific message about the countries’ relative costs for the goods. The United States has a unit labor cost advantage in producing pharmaceuticals ($3.75 compared to $5), whereas Japan has an advantage producing watches ($12.50 compared to $15). Thus, one would envision the United States specializing in pharmaceuticals and Japan in digital watches. The predicted pattern of trade would have the United States exporting the former product and importing the latter from Japan. Indeed, actual trade flows in the 1990s between the two countries displayed exactly this pattern.

Table 6.2 also carries a general message: Productivity matters, but it is not the only thing that matters. After all, according to the table, the United States has an absolute productivity advantage in both goods. Yet Japan turns out to have a cost advantage in watches. The cost edge materializes because Japan has a comparative advantage in watches. That is, Japan’s productivity disadvantage is much smaller in watches (where it is 80 percent as productive as the United States) than in pharmaceuticals (where it is only 50 percent as productive). After taking into account its lower wage rate, Japan indeed is the lower-cost watch producer.

Let us emphasize the point: Besides productivity, the countries’ relative wages and the prevailing exchange rate also matter. For instance, if U.S. wages increased more rapidly than Japanese wages over the coming year, the U.S. cost advantage in pharmaceuticals would narrow and Japan’s cost advantage in watches would widen. Alternatively, suppose productivities and wages were unchanged in the two countries, but the exchange rate changed over the year. For instance, suppose the value of the dollar rose to ¥125 per dollar. (We say that the dollar has appreciated or, equivalently, that the yen has depreciated.)